Build array

Visualization of Array Reponse

build_array ia a graphical interface for simple visualization of the array response function for a specific array geometry. The array reponse function is computed on a regular cartesian grid in the wavenumber domain ${\vec {k}}$ by evaluating:

$AR({\vec {k}}-{\vec {k}}_{0})=\|{\frac {1}{N}}\sum _{i=1}^{N}\exp(-j{\vec {r}}_{i}({\vec {k}}-{\vec {k}}_{0}))\|$

Here, $<{\vec {r}}_{i}/math>isthepositionvectorofsensoriinacartesiancoordinatesystem,<math>j$ the imaginary unit and ${\vec {k}}_{0}$ the true wavenumber vector of a single plane wave. As most seismological array applications are restricted to the deployment of sensors on the earth's surface, the above equation is evaluated in the horizontal plane, i.e. $<{\vec {r}}_{i}=(r_{ix},r_{iy})$ and ${\vec {k}}=(k_{x},k_{y})$ (horizontal wavenumber vector).

The evaluation of the array reponse function is simple, still the limits of the wavenumber range as well as the desired resolution for the grid computation $(\delta k_{x},\delta k_{y})$ needs to be specified. The resolution needs to be sufficient high in order to not miss small details of the peaked surface and the size of the grid should allow to determine the position of grating lobes or strong secondary side lobes in the 2D surface.